"Unable to connect to Apple TV"

Can anybody advise please why I always get the above message on my (fairly new) iPad when trying to connect to my just purchased 3rd Gen Apple TV to mirror the iPad screen? I'm tapping "Screen Mirroring" on the iPad Control Centre and then selecting "Apple TV" on the list. I've checked...

- that the Apple TV is on and not in standby (and has been restarted with the cable disconnected for 30 seconds)

- that AirPlay is set to "On" on the Apple TV

- that the Apple TV and iPad are connected to the same wi-fi network with a good signal

- that the Apple TV and iPad have the latest software (iPad has IOS 11.4.1 installed)

- that the Apple TV restrictions are turned off

- that Bluetooth is on (Apple TV just says "Searching...")

Thanks, any help will be appreciate.